Metallic strain gauges have been used as transducers for many years. More recently, semiconductor strain gauges have come into use having sensitivities that are hundreds of times greater than that of their metallic counterparts.
A strain gauge is typically used by bonding it to a flexible object and measuring the change in voltage across the gauge or the change in gauge resistance as different loads are applied to the object to vary the stress on the gauge. It is particularly advantageous to use a Wheatstone bridge in which two strain gauges are connected in series in one half of the bridge and two resistors are connected in series in the other half. Each of these four elements is in a separate arm of the bridge with the supply voltage applied to the nodes between the two halves and the output voltage measured between the node between the two resistors and the node between the two strain gauges. If the gauges are mounted on opposite sides of the object so that bending of the object applies a tensile loading (or stress) to one gauge and a compressive loading to the other, the ratio of the resistance of the two strain gauges is a function of the amount of deflection in the object. Hence, the output voltage from the bridge circuit can be related to the amount of deflection in the object. In a pressure-to-displacement transducer such as that shown in Birger B. Gabrielson's U.S. Pat. No. 4,172,388, which is incorporated herein by reference, this provides a convenient means of producing an output electrical signal which is a function of the pressure exerted by a fluid.
Ideally, a strain gauge should have the same resistance at any constant stress throughout its operating temperature range and its resistance should vary linearly with the stress that is applied. Thus, as shown in FIG. 1, a plot of strain gauge resistance (or voltage drop) versus temperature and stress is ideally a flat rectilinear surface 10. In practice, however, the resistance of a semiconductor strain gauge is a function of both stress and temperature and the plot of strain gauge resistance versus temperature and stress is neither flat nor rectilinear.
Practical semiconductor strain gauges are very sensitive to variations in temperature. For example, the resistance of a strain gauge at 180.degree. F. (82.degree. C.) may be twice that of a strain gauge at 0.degree. F. (-18.degree. C.) at the same pressure. Moreover, strain gauges have both a temperature coefficient of resistance and a temperature coefficient of gauge factor or sensitivity. Thus, both their resistance and their rate of change of resistance with applied stress vary with temperature. Even worse, the magnitude of both coefficients varies randomly from one gauge to the next; and the process of bonding the gauges is very likely to modify both the resistance and the temperature coefficients of the gauges. Thus, while it is possible to select matched pairs of semiconductor strain gauges whose temperature coefficients are approximately the same and to use such matched pairs in a bridge circuit to cancel out some errors due to variations in temperature, temperature effects still remain which will produce significant errors in the signal produced by the bridge circuit.
A plot of actual strain gauge resistance versus temperature and stress is typically a curved non-rectilinear surface such as a surface 15 of FIG. 1. As shown by surface 15, there are three types of error associated with the semiconductor strain gauge. First is the error in zero point, i.e., the variation A with temperature in the resistance of the strain gauge when the strain gauge is in the unstrained state. This error is random in both polarity and magnitude from one gauge to another. Second is the error in span, i.e., the variation B- (C-A) with temperature in the difference between the resistance of the strain gauge at maximum loading and its resistance in the unloaded, zero-point-corrected state. This error is uniform in polarity but random in magnitude from one gauge to another. The third error depicted by surface 15 is non-linearity of response with stress. As will be apparent, these variations in strain gauge resistance also lead to variations in the output voltage from the strain gauge bridge circuit.
Corrections are made for this variation in output voltage because of changes in resistance with temperature by measuring the resistance of the gauges under zero stress at two temperatures and selecting a series/parallel network of resistance for one gauge which offsets the effects of its temperature coefficient of resistance enough that the ratio of the resistance in the two strain gauge arms at the two compensation temperatures is identical. As a result, the output of the bridge circuit at zero stress is the same for both temperatures. This process is called two-point temperature compensation. It is also called zero or initial value compensation. Obviously, such compensation could be made instead at any other value of stress and accordingly this technique will be referred to generically as constant value compensation. As disclosed in my U.S. Pat. No. 4,172,389, which is incorporated hereby by reference, this technique can be extended so that the ratio of the resistances in the two strain gauge arms is substantially the same at three different temperatures, thereby providing three-point temperature (or constant value) compensation.
While such temperature compensation does improve the performance of the circuit as a measuring device, it does not guarantee that the resistance ratios are the same at any other temperature because of the complex effects of the temperature induced strain in the gauges. Moreover, temperature compensation alone makes no correction for the variation in output voltage because of change in sensitivity with temperature.
The variation in output voltage because of change in sensitivity with temperature may be compensated by the use of a span compensation resistance. The value of this resistance is selected to balance the temperature coefficient of sensitivity. More particularly, in one method, once the bridge is temperature compensated at its two compensation temperatures, its output voltage is measured at these two temperatures with maximum deflection being applied to the object on which the gauges are mounted. A resistor is then selected so that the output voltage under maximum stress is the same at both compensation temperatures. Alternatively, as shown in my U.S. Pat. No. 4,172,389, a value for the span compensation resistance can be determined from a series of measurements performed on the strain gauges when connected in series with an arbitrary resistance. These techniques generally are referred to as span compensation.
These techniques provide for span compensation at only two values of temperatures. Span compensation at other temperatures can be approximated by the use of a resistor-thermistor network as disclosed in John Raven's U.S. Pat. No. 4,174,639, which is incorporated herein by reference.
Despite the improvements in accuracy that can be achieved by two- and three-point temperature compensation and by span compensation, there is still substantial residual error at temperatures other than those where the compensation was made. The major causes of these errors are the non-tracking of the compensated gauges at temperatures other than the compensation temperatures, the inaccuracies in resistance of the compensation resistors, and the temperature coefficient of the resistors used for compensation as well as for the other elements in the bridge circuit. Other sources of error are the mismatch in the temperature offsets in the amplification of the output signal from the bridge, the temperature coefficient of the voltage source applied to the bridge, the mismatch between the true span error curve and the variable voltage provided by the resistor-thermistor network, and the temperature coefficients and inaccuracies in many other less critical components. For example, the cumulative effect of these errors may result in an error of 1/2% of full scale per 100.degree. F. (56.degree. C.) in the output of the bridge circuit under zero stress and up to 1% of full scale under other stresses. Moreover, as is apparent from the '389 and '639 patents, the improvements in accuracy that are achieved are won only at the cost of custom-tailoring the various compensation resistances to the idiosyncrasies of individual strain gauges.